How it works
This calculator finds the exact probability of each possible total when rolling several fair dice, by combining the dice one at a time. With two six-sided dice, 7 is the most likely sum: 6 of the 36 outcomes, or 16.67%.
Choose at least or at most to add up the probabilities on one side of the target, which is what you usually need for games (“roll 15 or higher on 3d6”).
As you add dice, the distribution of sums becomes more bell-shaped, an example of the central limit theorem. The chart shows up to 30 sums around the average.
Formula
P(sum = k) = (number of ways to roll k) ÷ sⁿ, found by convolving the single-die distribution n times
Questions people ask
What is the most likely sum with two dice?
7, with probability 6/36 = 16.67%. Sums of 2 and 12 are least likely at 1/36 = 2.78% each.
What are the odds of rolling 15 or more with 3d6?
20 of the 216 outcomes give 15–18, so the probability is 9.26%, about 1 in 10.8.
Does this assume fair dice?
Yes. Every face is assumed equally likely, and dice are independent of each other.